In a play we see everyone performing for everyone else on stage, as well as to the audience. Plays are highly rhetorical. In a play the soliloquy is the moment when the character, theoretically speaking to himself only but to the audience too, is considered to be speaking authentically his deepest thoughts. These cannot be lies unless the character is in a mode of self-deception. In a play like Hamlet, where everyone is trying "through indirections to find directions out," these moments of unadulterated thought are telling. For Hamlet, who has the most soliloquies by far, we can see not only the progression of his splendid mind but of the play's emerging themes as well.
By way of quick summary, let's line up the soliloquies you mention:
1.2: "O, that this too solid flesh would melt/ Thaw and resolve itself into a dew!" Here we first see Hamlet and hear of his grief that his father is dead and his mother remarried. He wishes he could die, and is disenchanted with the world and especially his mother. He knows that God has forbidden suicide and feels trapped in life to continue to suffer. This speech is laced with biting cynicism about the nature of life and is marked by Hamlet's sense of moral superiority.
2.2: "O, what a rogue and peasant slave am I!" Hamlet has just heard his beloved actors perform, and the Player King's moving monologue about Hecuba, Priam and the fall of Troy causes the actor to tear up. Hamlet chastises himself for having not acted on his own grief. He worries that he is failing his father and that he is a coward. He believes that he can confirm Claudius' guilt by staging a play that will stir his conscience, thus legitimating Hamlet's revenge.
3.2: "Tis now the very witching time of night." After the play, Hamlet feels authorized to take revenge and is filled with righteous anger, but he is first requested to visit his mother, to whom he means to "speak hot daggers."
3.3: "Now might I do it pat, now he is praying; And now I'll do't. And so he goes to heaven." On his way to his mother's chamber, Hamlet sees Claudius alone in prayer. This is the opportune time to kill him, but Hamlet stops because he does not want his revenge on Claudius to be a means to Claudius' going to Heaven. He decided to delay his revenge until he can catch him in a state of sin.
4.4: "How all occasions do inform against me, /And spur my dull revenge!" Having killed Polonius by mistake, Hamlet is being sent to England. On his way to the ship he sees Fortinbras's army and learns that young Norway is launching a battle over a piece of land of little worth. He does so for reputation or honor. This prompts Hamlet to again chastise himself for having failed to obey his father's command.
The one soliloquy omitted from the list is the 3.1, "To be, or not to be," which is the famous meditation on existence and what holds us back from suicide in an unjust world full of painful circumstances. This soliloquy is a speech that is focused on existence of "being." The arc of the play runs from Hamlet's initial claim that he "knows not seems" through this soliloquy to his later philosophical comment to "Let be."
The other soliloquies have a few things in common that give shape to that narrative and character arc. If 3.1 is about "being," the other soliloquies are about "doing": what one should do when confronted with an intolerable situation.
In Hamlet's case, the common theme running through these speeches all end up with his outrage at his father's murder and Gertrude's remarriage. "Frailty, thy name is woman" (1.2), "What's Hecuba to him, or he to Hecuba,/ That he should weep for her?" (2.2), "I will speak daggers to her." (3.2), "Up, sword; and know thou a more horrid hent:/ When he is drunk asleep, or in his rage,/Or in the incestuous pleasure of his bed" (3.3), and "How stand I then, /That have a father kill'd, a mother stain'd,/Excitements of my reason and my blood,/ And let all sleep?" (4.4). In these soliloquies a common reflection on the call to action he feels is also his delay, and the causes for it. Like the "To be or not to be" speech, Hamlet is a person whose mind is able to contemplate a multiplicity of factors with every thought and feeling, and this causes him to check his impulse to act as he recognizes the consequences of the act. In a traditional revenge tragedy, the protagonist would be moved to passion and would devise a means to execute the object of his revenge. Hamlet has this at multiple moments, yet he delays. The cause of these delays, as revealed in the soliloquies, reveal a superior mind and work to reduce the audience's appetite for bloody murder. With each soliloquy, Hamlet's and the audience's minds expand a bit regarding what it means to be human and how one might understand justice and revenge. Hamlet thinks about things so much, taking the simple idea of revenge and expanding it into a larger understanding of human existence and action. By the time he is done, the conventional revenge plot seems cliche, trite, and uninteresting. The times Hamlet does act rashly (killing Polonius, arranging the deaths of Rosencrantz and Guildenstern), he is less appealing than when he speaks to the audience about these difficult considerations that make his pause.
It is worth noting that Hamlet returns from England a different person. He is much calmer, more accepting of his fate, and able to muse on the parable of the sparrows from Matthew. In this passage, Hamlet displays an unusual peacefulness even while recounting the many offenses Claudius has committed against him:
There's a special providence in the fall of a sparrow. If it be now, 'tis not to come; if it be not to come, it will be now; if it be it not now, yet it will come. The readiness is all. Since no man knows aught of what he leaves, what is't to leave betimes
This is a remarkable acceptance that Hamlet could not have reached honestly had he not experienced all the agonizing self-doubt and introspection he describes in the earlier soliloquies. Far from being a simple desire to "tap out" of life's complexities, this is a steady-eyed recognition that life is marked by death and suffering, yet there is a plan behind it. It is a recognition that death and universal mortality is, as he heard in act 1.2 both "common" and "particular." The play has been a contemplation of death all along, and Hamlet finally is able to accept it, intellectually and experientially.
In the fencing scene, he is able to move to kill Claudius because he has direct evidence that Claudius is responsible for plotting another's death, rather than the suspicion and hearsay regarding the old King. Claudius dies through his own wicked plotting, and there is justice in that.
So, in review, the soliloquies all contemplate death, justice, and Hamlet's responsibility in addressing his father's murder and his mother's remarriage.